Dynamic column, simplified

If the solution were removed from Tank 1 and added to Tank 2, which also contained 1 eq of resin in the X ion form, the solution and resin phase would both contain 0.25 eq of Y ion and 0,75 eq of X ion. Repeating the procedure in a third and fourth tank would reduce the solution content of Y ions to 0.125 and 0.0625 eq. respectively. Despite an unfavorable resin preference. using a sufficient number of stages could reduce the concentration of Y ions in solution to any level desired. This analysis simplifies the column technique, but it does provide insights into the process dynamics. Separations are possible despite poor selectivity for the ion being removed. Most industrial applications of ion exchange use fixed-bed column... 

Operation of a batch distillation is an unsteady state process whose mathematical formulation is in terms of differential equations since the compositions in the still and of the holdups on individual trays change with time. This problem and methods of solution are treated at length in the literature, for instance, by Holland and Liapis (Computer Methods for Solving Dynamic Separation Problems, 1983, pp. 177-213). In the present section, a simplified analysis will be made of batch distillation of binary mixtures in columns with negligible holdup on the trays. Two principal modes of operating batch distillation columns may be employed ... 

The dynamic behavior of processes (pipe-vessel combinations, heat exchangers, transport pipelines, furnaces, boilers, pumps, compressors, turbines, and distillation columns) can be described using simplified models composed of process gains, dead times, and process dynamics. 

The problem of choosing whether and when to recycle each off-cut and the size of the cut is a difficult one. Liles (1966) considered dynamic programming approach and Luyben (1988) considered repetitive simulation approach to tackle this problem. Mayur et al. (1970) and Christensen and Jorgensen (1987) tackled it as a dynamic optimisation problem using Pontryagin s Maximum Principle applied to very simplified column models as mentioned in Chapters 4 and 5. 

The digital simulation of an extractive distillation column was performed in order to understand the dynamic behaviour of the system. Based on this results a considerably simplified dynamic model of sufficient accuracy could be developed. This model was employed in the design of a state observer and of an optimal control. After implementation in the large scale plant this new control system has proved to be highly efficient and reliable. 

In the presence of similar molecules and impurities, that molecule will also have to compete for the interactive sites on the surface of the stationary phase. The first scientist to assess the composite effects of mass transport in a chromatographic column from a chemical engineering perspective was JJ van Deem ter 241 in the early 1950s. In doing so he derived a more dynamic equation for the HETP which, in simplified form, can be represented as ... 

Lehr and Mewes [67] included a model for a var3dng local bubble size in their 3D dynamic two-fluid calculations of bubble column flows performed by use of a commercial CFD code. A transport equation for the interfacial area density in bubbly flow was adopted from Millies and Mewes [82]. In deriving the simplified population balance equation it was assumed that a dynamic equilibrium between coalescence and breakage was reached, so that the relative volume fraction of large and small bubbles remain constant. The population balance was then integrated analytically in an approximate manner. 

Nonlinear waves are very useful for a qualitative understanding of the concentration and temperature dynamics in an RD column. So far, only an incomplete understanding of the relation between the physicochemical complexity of the mixture, the design and operation of the column, and the observed spatiotemporal patterns is available. Much research is required to resolve the open issues. In addition, the phenomenon of a propagating wave can also be exploited to derive a simplified quantitative description of the column dynamics in the non-reactive [27, 67] as well as in the reactive [4, 51, 52] case. These reduced nonlinear models are most suitable to design and implement advanced model based control systems as discussed in the next section. 

Figure 23.6 shows a simplified system of fluid dynamics in bubble column bioreactors. The equations for the fluidized bed have been presented in Chapter 22, assuming the... 

Isakovic, T. Fischinger, M. 2006. Higher modes in simplified inelastic seismic analysis of single column bent viaducts. Earthquake Engineering and Structural Dynamics 35 95-114. 

Dynamic flowsheeting. The practical approach is to built a simplified dynamic model, but still capable to describe the relevant dynamics of the actual problem. Detailed dynamic models are necessary for the key units, where impurities are generated and eliminated, as kinetic models for reactors and dynamic models for some distillation columns. For units with... 

Heat generation also affects measurement of adsorption rate by batch techniques such as the gravimetric method. First, the effect of heat transfer rate on measurement of adsorption rate by a batch method is shown using a simple model as an example of nonisothermal effect. Then fundamental equations for heat transfer in packed beds are shown and simplified models presented. Estimation mehtods for heat transfer rate parameters in packed beds are introduced followed by a discussion of heat transfer in an adsorbent bed in adsorption equilibrium to show the coupling effect of heat and mass dispersion. Finally, the effect of heat transfer on adsorption dynamics in a column is illustrated using simple models. 

Simplified treatment of heat storage effect on column pressure dynamics... 

If the reboiler is either a well-agitated kettle type or a thermosyphcm type with a high recirculation rate, the reboiler/column-base composition dynamics are essentially those of a simplified basic tray (see Figure 18.1). The chief difference is that the reboiler has no entering vapor flow from a lower tray. Usually, too, the reboiler has considerably more holdup than a typical tray. The holdup, Af, is that of the reboiler itself plus that of the column base. 

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